Metamath Proof Explorer


Theorem simplbi2

Description: Deduction eliminating a conjunct. (Contributed by Alan Sare, 31-Dec-2011)

Ref Expression
Hypothesis simplbi2.1 ⊢ ( 𝜑 ↔ ( 𝜓 ∧ 𝜒 ) )
Assertion simplbi2 ( 𝜓 → ( 𝜒 → 𝜑 ) )

Proof

Step Hyp Ref Expression
1 simplbi2.1 ⊢ ( 𝜑 ↔ ( 𝜓 ∧ 𝜒 ) )
2 1 biimpri ⊢ ( ( 𝜓 ∧ 𝜒 ) → 𝜑 )
3 2 ex ⊢ ( 𝜓 → ( 𝜒 → 𝜑 ) )